General topology | Boolean algebra | Functors

Stone functor

In mathematics, the Stone functor is a functor S: Topop → Bool, where Top is the category of topological spaces and Bool is the category of Boolean algebras and Boolean homomorphisms. It assigns to each topological space X the Boolean algebra S(X) of its clopen subsets, and to each morphism fop: X → Y in Topop (i.e., a continuous map f: Y → X) the homomorphism S(f): S(X) → S(Y) given by S(f)(Z) = f−1[Z]. (Wikipedia).

Stone functor
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Related pages

Functor | Topological space | Category of topological spaces | Mathematics | Pointless topology | Clopen set | Stone's representation theorem for Boolean algebras | Category (mathematics) | Boolean algebra (structure)